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Harmonic curves

  1. Sep 13, 2004 #1
    Not sure if it's called "curves" in English, but what I am refering to is graphs that repeat over a given time.
    f(x) = sin(x)

    The problem I am having is understanding the following:
    f(x) = sin(x)
    g(x) = cos(x)

    Find f(x) - g(x) by A(cos(x - x0)).
    Which gives:
    A(cos(x - x0)) = A(cos(x0))cos(x) + A(sin(x0))sin(x)
    A(cos(x0)) = 1
    A(sin(x0)) = -1

    A = sqrt(1^2 + (-1)^2) = 1

    Finding x0:
    tan wx0 = 1/(-1)
    1*x0 = arctan(-1)
    x0 = -0.79

    Here I'm pretty much lost. I've probably done some mistakes along the way as well :(
    What is -0.79? x0 is supposed to be the 'top' of the curve right?
    ie to find every top, you would have something like:
    x0 +/- |n|*2PI

    Where n is a whole number(1..inf) and 2PI would be the period of each "curve".

    Could someone explain this to me, I'm trying to learn this by just reading a book and I'm having a hard time.
  2. jcsd
  3. Sep 13, 2004 #2
    sqrt(2) is sqrt(2), not 1 :rolleyes:
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